We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.

We will demonstrate the utility of Monte Carlo integration by using this algorithm to calculate an estimate for . In order to improve this estimate, we will also demonstrate how a family of covariate functions can be used to reduce the variance. Finally, the optimal covariate function within this family is found numerically. 1. An Introduction to Monte Carlo Integration 1.1. Monte Carlo Integra...

The common numerical problem in Bayesian analysis is the numerical integration of the posterior. In high dimensions, this problem becomes too formidable for xed quadrature methods, and Monte Carlo integration is the usual approach. Through the use of modal standardization and a spherical-radial transformation, we reparameterize in terms of a radius r and point z on the surface of the sphere in ...